2019/09/29 by Roberto Fernández, Fernández, Roberto, Nguyen Tong Xuan +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Phase Equilibria and Thermodynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1909.13257
openalex publication_date 2019/09/29 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We study the convergence of cluster and virial expansions for systems of\nparticles subject to positive two-body interactions. Our results strengthen and\ngeneralize existing lower bounds on the radii of convergence and on the value\nof the pressure. Our treatment of the cluster coefficients is based on\nexpressing the truncated weights in terms of trees and partition schemes, and\ngeneralize to soft repulsions previous approaches for models with hard\nexclusions. Our main theorem holds in a very general framework that does not\nrequire translation invariance and is applicable to models in general measure\nspaces. For the virial coefficients we resort to an approach due to Ramawadth\nand Tate that uses Lagrange inversion techniques only at the level of formal\npower series and leads to diagrammatic expressions in terms of trees, rather\nthan the doubly connected diagrams traditionally used. We obtain a new\ncriterion that strengthens, for repulsive interactions, the best criterion\npreviously available (proposed by Groenveld and proven by Ramawadth and Tate).\nWe illustrate our results with a few applications showing noticeable\nimprovements in the lower bound of convergence radii.\n